Why does a higher i compensate for higher systematic risk. Surely it also reduces the value of negative cashflows which would increase the NPV?

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In the context of capital projects a higher discount rate is a quick and relatively simple way to compensated for risk. The reason why this is the case is that the higher the discount rate the lower the NPV for future cashflows - this illustrates the riskiness of cashflows that occur far into the future.

You are correct in that the higher discount rate will also reduce the value of the negative cashflows. However, in most capital projects most of the negative cashflows (costs associated with setting up the project) occur at and around the start of the project which results in the discount rate not having that much of an effect on the NPV for these cashflows. Other negative cashflows that occur regularly would be running expenses that are typically much lower than the initial costs, making them not very sensitive to the discount rate assumption.

If the project is expected to have rather large negative cashflows at later dates then a high discount rate would unduly suppress their effect on the NPV. Other methods to account for this would then be advised, e.g. attaching probabilities to the negative cashflows to account for their risk and using a lower discount rate.

For another discussion around the use of the discount rates to account for risk refer to a question asked here.

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